We have explored the influence of different matrices on the emission line shape of individual homogeneously coated CdSe/CdS/ZnS nanocrystals. The results obtained corroborate previous observations of a correlation between blinking events and spectral diffusion but in addition we have found that the extent of spectral diffusion is almost independent of the dielectric environment of the NC. Additionally, we report the observation of a correlation between the line width and emission energy which is not expected to occur in the spherical - symmetric NCs employed in this work. The implications of these results are discussed. ; Comment: 3 pages, 3 figures